## Step (1)

The table below shows

all the whole numbers squared

in the left column

&

the respective triangular numbers

generated from these

in the right column.

##### Triangular Numbers Table

##### Base

number

##### Triangular

number

0

(0 x 1)/2 = 0

1

(1 x2 )/2 = 1

4

(4 x 5)/2 = 10

9

(9 x 10)/2 = 45

16

(16 x 17)/2 = 136

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0 = 0

0 + 1 = 1

0 + 1 + 10 = 11

0 + 1 + 10 + 45 = 56

0 + 1 + 19 + 45 + 136 = 192

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60(0) + 1 = 1

60(1) + 3 = 63

60(11) + 5 = 665

60(56) + 7 = 3367

60(192) + 9 = 11529

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1 = 1 = 16

1 + 63 = 64 = 26

1 + 63 + 665 = 729 = 36

1 + 63 + 665 + 3367 = 4096 = 46

1 + 63 + 665 + 3367 + 11529 = 15625 = 56

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one can deduce that in general

n to the 6th. power is

the summation of triangular numbers

per the formula shown below: